Critical Phenomena and Field Theory

John Cardy

The use of field theoretic methods to study problems in critical phenomena
has a long history, dating back to the 1970's. Field theory provides a natural
framework incorporating ideas of scaling and the renormalisation group
which explain much of the phenomenology of critical phenomena, as well as
providing an approximate calculational scheme. In the 1980's this was
supplemented by the powerful
methods of conformal and integrable
field theory which
give exact information on many classical systems in two dimensions (and
one-dimensional quantum systems).

I have for some time been involved
in the development of this theory as applied to quenched random systems
(for example,
random magnets
and
disordered electronic systems)
as well
as to 'geometric' critical behaviour such as
percolation
and
self-avoiding walks,
which model polymers.
A new development is this area is the description of the random curves
which arise in these systems using stochastic Loewner evolution
(SLE).
Much of the this work is
fairly mathematical, but the aim is always to derive results of physical
significance, which can be tested against experiment or numerical
simulation.

Another aspect of my work in the 1990s was the
application of systematic field-theoretic renormalisation group methods
to non-equilibrium critical behaviour, particularly in
reaction-diffusion
systems. Recently I have collaborated on applications in
biology.

Another recent interest is the computation of entropy as a measure of
quantum entanglement in extended systems.